Saturday night (I think it was Saturday) some friends and myself were watching the end of the 'Earth Day’special on ABC hosted by Leonardo DiCaprio. (We were actually waiting for it to end so we could jump to the movie we wanted to watch at 8).
Anyway, at the end Leonardo mentions the butterfly effect and how it can cause a hurricane somewhere in the world. Ergo…any action, no matter how insignificant, can have HUGE consequences.
I mention that this is nonsense and explain to my friends the the butterfly effect is merely an illustration of how difficult it is to predict complex systems. The idea being that if you could program a really powerful computer with ALL of the relevant info on the earth’s atmosphere at a given point it could theoretically predict the weather with 100% certainty. BUT, if you missed so much as a butterfly flapping its wings eventually the computer would fail to predict a hurricane. But, it cannot be said that the butterfly CAUSED the hurricane.
My friend, however, disagreed. He said that if you can account for ALL variables except the butterfly flapping and a hurricane gets missed somewhere down the road then it can truthfully be said that the butterfly ‘caused’ the hurricane. I can see the butterfly being one of several billion (or insert REALLY big number here) events that added up to the hurricane but it was a failure in prediction and not a causal effect that the butterfly engendered.
So, are Leonardo and my friend correct or do I have the right of it? In either case if you can point out the fallacy in the arguments that would be great.
If you have a situation of this type you have sensitive dependence on initial conditions. This means that an arbitrarily small change or error in the measurement of initial conditions results in your model’s prediction being out by a large amount. The butterfly is illustrative of the impossiblity of precisely specifying initial conditions in a real world non-linear dynamical system, so you would never have all the information you require except the butterfly’s flapping.
The notion of cause is fairly tricky, and I’d steer clear of it if I were you. Build a model where all variables are endogenous except the butterfly flap which can be set to 0 or 1: it done it. But remember that the butterfly’s position and need to flap at that time is at least partly due to the operation of the system up to that point. There is complex interdependence here.
But I’m willing to bet DiCaprio isn’t responsible.
Are you sure? Do the computer simulations take into account the mass movement of air caused by teenie-boppers flocking to see his next movie? I’d wager that Leo’s flapping gums have just as much effect on the weather as any given butterfly…
In a complex system with huge numbers of independent or interrelated variables, “causation” is a tricky concept.
Generally speaking hurricanes, tornadoes, and other dramatic weather events are “caused” in general by the heating of the atmosphere by the sun and the stirring of the atmosphere by the rotation of the earth. This model of causation seems more compelling because the heating and stirring pump in the necessary energy to cause weather phenomena.
It’s probably irrelevant to argue what causes a specific instance of a phenomenon in such complicated circumstances. All small events “cause” a particular instance; to elevate one such small event and call it “different” than the others is clearly an error.
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam.
I think you and your friend are both right. The way I always interpreted the butterfly effect was:
A small factor will come into play, be magnified by the other factors (in such a way you haven’t allowed for) and your predictions will be wrong. In this instance, you can say the small factor “caused” the outcome, but to be more accurate, lots of things contributed to the outcome, which together caused it, not merely one thing.
It does not necessarily mean you missed something while predicting a complex system, merely explains why complex systems are so hard to predict.
The origin of the phrase “Butterfly Effect” is covered in the book Chaos: The Making of a New Science by James Gleick. I don’t have the book in front of me, but it went something like this.
In the early 1960’s a group of scientist were doing weather research using a simplified computer model of the atmosphere. The model displayed its output as a string of numbers on a teletype.
For some reason, the group had to re-run part of the model. Since they did not want to restart from the beginning (the model was complex and the computer running it was slow) they entered the values from the middle of the run from the printout and restarted the model at that point.
They expected the model to pick up from the point they entered the data, but to their surprise they found that the model rapidly diverged from the initial run and, in just a few cycles, was giving completely different results.
Investigation showed that the model internally was keeping six places after the decimal but the printout was only displaying three. When they re-entered the values to re-start the run they were therefore off by a few ten-thousanths. This was enough to cause the model to produce completely differnet results. One of the scientists described the magnitude of the changes as being something like “a butterfly flapping its wings in China causing a hurricane to hit New York.” (Quote approximate)
In Chaos theory the phrase “Butterfly Effect” has come to mean that, in a chaotic system, a very small change in input can cause a very large change in output.
I’ll dig the book out this evening if anyone needs any more details.
“Sometimes I think the web is just a big plot to keep people like me away from normal society.” — Dilbert
The book Chaos is actually a decent read and helps put things like the butterfly effect into perspective. It makes the point that weather prediction is still so incredibly difficult because of how the big picture is made of bazillions of tiny elements. To make true preditions we’d not only need a much deeper understanding of the system but be able to measure the energy state of nearly every particle in it to do a halway decent job.
An exaple that better illustrates the butterfly effect from the book was a researcher doing computer modeling of a weather system. He needed to repeat a run but instead of starting at the beginning with the same variables he started in the middle with the variables generated at that point in the original run. The end resulst was vastly different because of tiny rounding errors in the stored values that were thought to be insignificant. It’s not that a butterfly will cause a hurrican but that to really predict the weather you’d need to know all the butterflies (and raindrops and puffs of wind) are doing.
Ray Bradbury’s short story “A Sound of Thunder” is the original source of the term “butterfly effect,” and may have inspired that scientist to choose that particular analogy. In the story, the crushing of a prehistoric butterfly on the boot of a time traveler changed a presidential election (and presumably a whole bunch of other things) in the future. With time-traveling hindsight, causation was easy to determine.
Gleick points out that having perfect measurements of the weather conditions at 1’ (yes, that’s 12 inches) intervals everywhere on the face of the globe would still only allow 5 days of accurate forecasting. After that, the inherent uncertainty makes precise prediction impossible, although generalities are still fine (like, no snow in the Sahara in August).
This rules out specific causation completely: you can never know all of the initial conditions, so you can never know if the presence or absence of one of them (e.g., the butterfly) caused the hurricane, much like Padeye said.
I lead a boring life of relative unimportance. Really.
That’s certainly not clear to me. Let’s try two different experiments, exactly the same except one has the butterfly. Wait a while, and the differences will be greater than just a hurricane. If the only initial difference was the butterfly, the butterfly, in a valid sense, could be said to have caused the eventual great differences.
After hanging around the Time Travel thread, it just occurred to me: you need time travel in order to observe the butterfly effect. We’ve already established that it’s impossible to recreate the initial conditions. That’s what led to the discovery of this problem in the first place. You simply can’t perform any experiment a second time with only the addition of a butterfly. Restoring everything (including planetary alignment!) to its original state effectively is time travel (and/or omnipotence).
Remember, you are part of the system as well (Schroedenger’s cat’ll back me up on this). Every gesture, breath, eye blink, pencil scratch, thoughtful pause; all must be identical. In other words, your restored self would have no idea to stick a butterfly in the experiment the 2nd time around. You’d get stuck in an endlessly repeating loop, running the same experiment over and over forever.
Oh, and sorry for the excessive use of emphasis: it’s the caffeine talkin’.
I buy what you’re saying. But as a thought experiment is RM Mentock correct?
Assume we can ‘magically’ recreate the exact conditions. If the presence of the butterfly in in the second experiment results in a hurricane (where there wasn’t a hurricane in the first experiment) then can it be said the butterfly ‘caused’ the hurricane?
When put in terms like that it seems as if the butterfly does cause the hurricane but something bugs me (no pun intended) about this. It feels like there is a flaw in logic somewhere but I can’t find it (never mind that one of the ‘flaws’ is that this experiment would never work).
Suppose you “magically” restore the butterfly and the hurricane reappears. Thus the butterfly caused the hurricane, right?
But now you rerun the experiement with the butterfly, but you have Homer Jenkins of Podunk IL hold his breath for 30 seconds. Whoops! The hurricane went away again!
You repeat the experiment 1,000 times, and each time some small factor, by itself, “causes” or “prevents” the hurricane.
Which small event “caused” the hurricane? Note that they all didn’t cause it; if you remove all the small causes, the hurricane reappears! This experiment shows why small effects shouldn’t be considered a “cause” in the ordinary sense of the word.
Regardless of these microscopic events, all of the macroscopic conditions are in place for the formation of the hurricane. The hurricane will appear sooner or later, somewhere or another. The microscopic events contribute only to the details of the particular expression.
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam.
Of course, any instrument which measures the initial variables and starting positions of elements of a system must, itself, occupy space. This space, that taken up by the measuring device, will contains unknowns and uncertainties. These will eventually grow to become arbirtrarily large - larger than the outcomes that were anticpated from the initial measurement. (The device will also give off heat making things worse)
BTW, I have always been distressed that some books and articles on chaos etc. use a prominent illustration of an attractor that could be said to resemble a butterfly. I have heard some people state, incorrectly, that this depicts the “butterfly effect”.
Though Ray Bradbury did indeed write about a butterfly causing great changes in history, and did it well before chaos theory needed the descriptive term, there’s no evidence there is any connection between his story and the coining of the phrase (which does not appear anywhere in the story).
“What we have here is failure to communicate.” – Strother Martin, anticipating the Internet.
This sounds like the old rhyme"for want of a shoe…the kingdom was lost"
Do people make history or are there impersonal forces that determine the flow of history? This question has been posed by philosophers-suppose Adolf hitler had been killed in WWI-would the Nazi horror of the Third Reich ever come in to existence?
Will what I have for breafast tomorrow determine the fate of millions, a hundred years hence?
egkelly: Everything you do, and everything you don’t will have profound and completely unpredictable effects on the future. Since the effects are totally unpredictable, you might as well just do as you would, without regard to the potential consequences.
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam.
There was a short story I read years ago about the Butterfly Effect.
A time-travel agency had set up anti-grav platforms in the dinosaur age so that big game hunters could go hunting the biggest game ever. The agency would locate a dino that was about to die anyway, then take the safari to minutes before its demise to blast it, all the while staying on their anti-grav platform. (They also had to go dig all their bullets out of the dino.)
One hunter gets freaked out and runs off the platform during the hunt. The guide finds him and takes him back to the future. But the future is different, with the US gov’t replaced by a Nazi-like one. The hunter looks down at his boots, which are covered with mud. Looking on the underside, there is a butterfly that he stepped on. Somehow its premature demise affected human politics millions of years later.
Yeah, AWB, that’s the Bradbury story “A Sound of Thunder” referred to in numerous previous posts.
RealityChuck: of course the story didn’t mention the words “butterfly effect,” and I know, via Gleick, of the supposed origin of the term. I was speculating on the scientist’s choice of words being somehow related to the far older story. Scientific magazines of the time made references to Bradbury’s concept, so it could have been as well ingrained in the subconscious of that guy as it was in my own.
Jeff_42: using the magic of the thought experiment to remove yourself as a variable should allow the butterfly to be causal as RMM suggested. I was appreantly in a devil’s advocate sort of mood. Arguments along the lines of “other minor variables will also cause the hurricane so you can’t nail the butterfly as the cause” won’t wash: it’s a thought experiment, where we explicitly stated that we held everything but the butterfly unchanged.
Terry Pratchett, in INTERESTING TIMES, writes about "…the butterfly of the storms.
"See the wings, slihgtly more ragged than those of the common fritillary. In reality, thanks to the fractal nature of the universe, this means that those ragged edges are infinite – in the same way that the edge of any rugged coastline, when measured to the ultimate microscopic level, is inifinitely long – or, if not infinite, then at least so close to it that Infinity can been on a clear day.
"And therefore, if their edges are infinitely long, the wings must logically be infinitely big.
"They may look about the right size for a butterfly’s wings, but that’s only because human beings have always preferred common sense to logic.
"The Quantum Weather Butterfly (Papilio tempestae ) is an undistinguished yellow colour, although the mandelbrot patterns on the wings are of considerable interest. Its outstanding feature is its ability to create weather.
“This presumably began as a survival trait, since even an extremely hungry bird would find itself inconvenienced by a nasty localized tornado.* From there it possibly became a secondary sexual characteristic, like the plumage of birds or the throat sacs of certain frogs. Look at >me, the male says, flapping his wings lazily in the canopy of the rain forest. I may be an undistinguished yellow clour but in a fortnight’s time, a thousand miles away, Freak Gales Cause Road Chaos.”
Usually about six inches across
That should answer, once and for all, everything you need to know about butterflies causing storms.
[Note: This message has been edited by CKDextHavn]